论文标题
双曲机平面中Voronoi渗透的关键可能性往往$ 1/2 $
The critical probability for Voronoi percolation in the hyperbolic plane tends to $1/2$
论文作者
论文摘要
我们考虑在双曲平面上由均匀的泊松点过程产生的Voronoi Tessellation上的渗透。我们表明，由于泊松过程的强度倾向于无穷大，因此无限集群存在的关键可能性往往$ 1/2 $。这证实了本杰米尼和施拉姆的猜想。
We consider percolation on the Voronoi tessellation generated by a homogeneous Poisson point process on the hyperbolic plane. We show that the critical probability for the existence of an infinite cluster tends to $1/2$ as the intensity of the Poisson process tends to infinity. This confirms a conjecture of Benjamini and Schramm.
